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KCET2020MathematicsContinuity and Differentiability

If f(x)= | array ccc x³-x & a+x & b+x x-a & x²-x & c+x x-b & x-c & 0 array | , then

Options

  1. Af( l )=0
  2. Bf(2)=0
  3. Cf(0)=0
  4. Df(-1)=0

Correct answer

C. f(0)=0

Step-by-step solution

We have, aligned f(x) &= | array ccc x³-x & a+x & b+x x-a & x²-x & c+x x-b & x-c & 0 array | f(0) &= | array ccc 0 & a & b -a & 0 & c -b & -c & 0 array | f(0)=0 & aligned f(0) is skew symmetric matrix of order 3 .

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